Much beyond Mantel: Bringing Procrustes Association Metric to the Plant and Soil Ecologist’s Toolbox

Abstract

The correlation of multivariate data is a common task in investigations of soil biology and in ecology in general. Procrustes analysis and the Mantel test are two approaches that often meet this objective and are considered analogous in many situations especially when used as a statistical test to assess the statistical significance between multivariate data tables. Here we call the attention of ecologists to the advantages of a less familiar application of the Procrustean framework, namely the Procrustean association metric (a vector of Procrustean residuals). These residuals represent differences in fit between multivariate data tables regarding homologous observations (e.g., sampling sites) that can be used to estimate local levels of association (e.g., some groups of sites are more similar in their association between biotic and environmental features than other groups of sites). Given that in the Mantel framework, multivariate information is translated into a pairwise distance matrix, we lose the ability to contrast homologous data points across dimensions and data matrices after their fit. In this paper, we attempt to familiarize ecologists with the benefits of using these Procrustean residual differences to further gain insights about the processes underlying the association among multivariate data tables using real and hypothetical examples.

Application of multivariate statistical techniques in microbial ecology

“…Significance of the linear relationship between matrices is assessed through permutation of objects (see Box 6). The goal of Mantel test is similar to that of CCorA, CIA, and PA (Lisboa et al , 2014). …”

The role of plant mycorrhizal type and status in modulating the relationship between plant and arbuscular mycorrhizal fungal communities

“…Procrustes residuals – the residuals derived from Procrustes correlation – were used to assess variation in correlation strength (Lisboa et al ., ) among successional stages and in relation to the abundance of AM fungi (NLFA 16:1ω5) and plant AM status. Variation in Procrustes residuals in relation to these explanatory variables was modelled using linear mixed‐effect models with the same structure as described above for successional shifts in species richness and abundance of AM fungi and plants.…”

Changes in ectomycorrhizal fungal community composition and declining diversity along a 2‐million‐year soil chronosequence

“…To explore whether shifts in plant composition were related to shifts in ECM fungal community composition, we performed a Procrustes test (Lisboa et al . ) between vegetation and ECM fungal OTU matrices. Vegetation data from the same plots were obtained from Laliberté et al .…”